Different kinds of wave packet transforms are widely used for extracting multi-scale structures in signal processing tasks. This paper introduces the quantum circuit implementation of a broad class of wave packets, including Gabor atoms and wavelets, with compact frequency support. Our approach operates in the frequency space, involving reallocation and reshuffling of signals tailored for manipulation on quantum computers. The resulting implementation is different from the existing quantum algorithms for spatially compactly supported wavelets and can be readily extended to quantum transforms of other wave packets with compact frequency support.

翻译：不同类型的波包变换广泛应用于信号处理任务中的多尺度结构提取。本文提出了一类具有紧频支撑的波包（包括Gabor原子和小波）的量子电路实现方法。我们的方法在频域空间中进行操作，涉及为量子计算机操控而设计的信号重分配与重组。该实现方案不同于现有针对空间紧支撑小波的量子算法，并且可便捷地推广至其他具有紧频支撑波包的量子变换。